**Naval Research Logistics (NRL)**

# Signature based analysis of *m*-Consecutive-*k*-out-of-*n*: *F* systems with exchangeable components

## Abstract

In this article, we study reliability properties of *m*-consecutive-*k*-out-of-*n*: *F* systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature-based stochastic ordering results for the system's lifetime and investigate the *IFR* preservation property under the formulation of *m*-consecutive-*k*-out-of-*n*: *F* systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011